Inverse Problem for a Partial Differential Equation with Gerasimov–Caputo-Type Operator and Degeneration

Abstract

In the three-dimensional open rectangular domain, the problem of the identification of the redefinition function for a partial differential equation with Gerasimov–Caputo-type fractional operator, degeneration, and integral form condition is considered in the case of the 0α≤1 order. A positive parameter is present in the mixed derivatives. The solution of this fractional differential equation is studied in the class of regular functions. The Fourier series method is used, and a countable system of ordinary fractional differential equations with degeneration is obtained. The presentation for the redefinition function is obtained using a given additional condition. Using the Cauchy–Schwarz inequality and the Bessel inequality, the absolute and uniform convergence of the obtained Fourier series is proven.

Keywords

• inverse problem
• Gerasimov–Caputo-type fractional operator
• redefinition function
• degeneration
• integral form condition
• one value solvability